Transcript sidis
A sideways look into the proton
Transverse momentum and transverse spin in QCD
Alessandro Bacchetta
Outline
•
•
•
•
Introduction
Transverse spin
Transverse momentum
Transverse spin and transverse
momentum
• Factorization and hadron collisions
• Conclusions
Alessandro Bacchetta
A sideways look at the proton
2/60
Introduction
Deep Inelastic Scattering - DIS
electron
target proton
Alessandro Bacchetta
A sideways look at the proton
4/60
Inclusive DIS
(l ) p (P ) (l ) X
(l l ')2 Q 2 virtuality of photon
l'
Q2
x
2P ( l l ')
lepton
transverse
proton
l
longitudinal
Alessandro Bacchetta
A sideways look at the proton
5/60
Semi-inclusive DIS (SIDIS)
(l ) p (P ) (l ) h(Ph ) X
(l l ')2 Q 2 virtuality of photon
l'
Q2
x
2P ( l l ')
proton
lepton
Ph
l
P Ph
z
P (l l ')
Alessandro Bacchetta
pion
Ph transverse momentum of pion
A sideways look at the proton
6/60
Vectors and angles involved
DIS
Alessandro Bacchetta
A sideways look at the proton
7/60
Vectors and angles involved
SIDIS
Alessandro Bacchetta
A sideways look at the proton
8/60
Transverse momentum effects
Drell-Yan
SIDIS
Ph
KT
qT
p-p to pions
3-D
e-e+ to pions
Whenever we measure transverse-momentum effects, we need
kT-factorization and we need transverse momentum dependent
(or unintegrated) parton distributions
Collins, Soper, NPB 193 (81)
RT
Alessandro Bacchetta
A sideways look at the proton
9/60
Feynman diagrams & Factorization
lepton
lepton
proton
pion
SIDIS
Partonic scattering
amplitude
Fragmentation amplitude
Distribution amplitude
Alessandro Bacchetta
A sideways look at the proton
10/60
Feynman diagrams & Factorization
lepton
lepton
proton
lepton
proton
pion
proton
antilepton
SIDIS
Drell-Yan
electron
pion
Partonic scattering
amplitude
Fragmentation amplitude
positron
e–e+
pion
to pions
Alessandro Bacchetta
A sideways look at the proton
Distribution amplitude
11/60
Feynman diagrams & Factorization
lepton
lepton
proton
lepton
proton
pion
proton
antilepton
SIDIS
Drell-Yan
electron
pion
proton
positron
pion
proton
e–e+ to pions
Alessandro Bacchetta
A sideways look at the proton
pion
?
pion
p-p to pions
12/60
Nonperturbative elements
k
2
=
P, S
d i x P
ij ( x; S )
e
P, S j (0) U[0, ] i ( ) P, S
2
Alessandro Bacchetta
A sideways look at the proton
0
13/60
Decomposition of the
correlation function
O(1 Q0 ), leading twist
( x; S )
1 q
f1 ( x ) g1q ( x ) 5 SL h1q ( x ) 5S T
2
f1q ( x ) q( x )
Unpolarized distr. func.
g1q ( x ) q( x )
Helicity distr. func.
h1q ( x ) q( x ) T q( x )
Transversity distr. func.
Alessandro Bacchetta
A sideways look at the proton
14/60
Longitudinal vs transverse momentum
Long. view
Trans. view
Photon moves into the screen/
proton moves out of the screen
kparton
kT
photon
parton
P
klong xP
photon
target
long. spin
Alessandro Bacchetta
A sideways look at the proton
15/60
Longitudinal vs transverse momentum
Long. view
Trans. view
Photon moves into the screen/
proton moves out of the screen
kparton
kT
photon
parton
P
klong xP
photon
trans. spin
Alessandro Bacchetta
target
A sideways look at the proton
16/60
Probabilistic interpretation
Photon moves into the screen/
proton moves out of the screen
f ( x ) q( x )
q
1
g ( x ) q ( x )
q
1
h ( x ) T q ( x )
q
1
Alessandro Bacchetta
A sideways look at the proton
_
_
17/60
Decomposition of the correlation
function UNintegrated over kT
Mulders, Tangerman, NPB 461 (96)
Goeke, Metz, Schlegel, PLB 618 (05)
T ST kT
1 q
2
q
2
( x, kT )
f1 ( x, kT ) f1T ( x, kT )
2
M
T
q
2 k
i h1 ( x, kT ) ...
M
Sivers, PRD 43 (91)
Boer, Mulders, PRD 57 (98)
Alessandro Bacchetta
A sideways look at the proton
18/60
Probabilistic interpretation
Photon moves into the screen/
proton moves out of the screen
Sivers
-
Boer-Mulders
-
Alessandro Bacchetta
A sideways look at the proton
19/60
Unpolarized distribution functions q(x)
ZEUS Coll, EPJ C42 (05)
7 groups are working on the extraction of these PDFs
(see www-spires.dur.ac.uk/hepdata/pdf.html)
Alessandro Bacchetta
A sideways look at the proton
20/60
Helicity distribution function q(x)
AAC, Hirai et al. PRD69 (04)
6 groups are working on the extraction of these PDFs
(see www-spires.dur.ac.uk/hepdata/pdf.html)
Alessandro Bacchetta
A sideways look at the proton
21/60
• What about the transverse spin
distribution h1(x) ?
• What about the transverse momentum
dependence, e.g. f1(x,kT2)?
Alessandro Bacchetta
A sideways look at the proton
22/60
Transverse spin
Transversity in SIDIS
d
... ST sin(h S ) h1 ( x, pT2 ) H1 ( z, kT2 ) ...
see e.g. A.B., Diehl, Goeke, Metz,
Mulders, Schlegel, JHEP 0702,093
Alessandro Bacchetta
A sideways look at the proton
24/60
Data from Hermes and Compass
DEUTERON
PROTON
HERMES, hep-ex/0507013
COMPASS, NPB 765 (07)
HERMES, PRL 94 (05)
COMPASS, PRL 94 (05)
Alessandro Bacchetta
A sideways look at the proton
25/60
Data from BELLE
BELLE, PRL 96 (06)
Alessandro Bacchetta
A sideways look at the proton
26/60
First extraction of transversity
Anselmino et al., PRD 75, 054032 (07)
Alessandro Bacchetta
A sideways look at the proton
27/60
Comparison with some models
[1] Soffer et al. PRD 65 (02)
[4] Wakamatsu, PLB 509 (01)
[2] Korotkov et al. EPJC 18 (01)
[5] Pasquini et al., PRD 72 (05)
[3] Schweitzer et al., PRD 64 (01)
[6] Anselmino et al., PRD 75 (07)
Alessandro Bacchetta
A sideways look at the proton
28/60
Tensor charge from Lattice QCD
Compared to
axial charge
u h1u ( x)dx 0.84,
d h1d ( x)dx 0.23,
u g1u ( x)dx
d g1d ( x)dx
0.64,
0.35
S. Aoki et al., PRD 56 (1997)
M. Göckeler et al. [QCDSF/UKQCD], PLB (05)
Alessandro Bacchetta
A sideways look at the proton
29/60
Comparison of tensor charges
c quark
spectator
2.4 GeV2
non-relativistic
lattice
0.3 GeV2
bag
c quark soliton 2
c quark soliton 1
Wakamatsu, 0705.2917[hep-ph]
Alessandro Bacchetta
Barone, Drago, Ratcliffe, PR 359 (2002)
A sideways look at the proton
30/60
Evolution equations
Barone, Drago, Ratcliffe, PR 359 (2002)
Hayashigaki, Kanazawa, Koike, PRD56 (97)
Alessandro Bacchetta
A sideways look at the proton
31/60
Other observables
d
... ST sin(h S ) h1 ( x, pT2 ) H1 ( z, kT2 ) ...
Dihadron fragmentation
Efremov, Mankiewicz, Tornquist, PLB 284 (92)
Collins, Heppelmann, Ladinsky, NPB 420 (94)
Jaffe, Jin, Tang, PRL 80 (98)
d
... ST sin(h R ) h1 ( x ) H1 ( z, , M ) ...
2
Doubly polarized Drell-Yan
d
Alessandro Bacchetta
Ralston, Soper, NPB 152 (79)
... S1T S2T h1 ( x1 ) h1( x2 ) ...
A sideways look at the proton
32/60
Transverse momentum
Semi-inclusive DIS
l p l X
(l l ')2 Q 2 virtuality of photon
l'
proton
lepton
Ph
l
pion
Ph transverse momentum of pion
Alessandro Bacchetta
A sideways look at the proton
34/60
Example of model calculation
quark
diquark
proton
Jakob, Mulders, Rodrigues, NPA 626 (1997)
f1q ( x, kT2 )
f1q ( x, kT2 )
x 0.5
ky
x 0.01
ky
k x (GeV)
k x (GeV)
kT2 0.13 GeV 2
Alessandro Bacchetta
A sideways look at the proton
kT2 0.48 GeV 2
35/60
Example of a measurement
H1 Coll, NPB485(97)
Alessandro Bacchetta
A sideways look at the proton
36/60
Transverse momentum distribution
h
fragmentation
q
q
pQCD
intrinsic
Koike, Nagashima, Vogelsang, NPB744 (06)
Alessandro Bacchetta
A sideways look at the proton
37/60
Differences between flavors?
u
proton
d
ud diquark
uu diquark
proton
Assuming Mud Muu
f1d (kT2 )x 2
f1u (kT2 )
ky
ky
k x (GeV)
Alessandro Bacchetta
A sideways look at the proton
k x (GeV)
38/60
Transverse momentum and
transverse spin
Semi-inclusive
Deep Inelastic Scattering
l p l X
left
l'
lepton
proton
l
N N
NR NL
R
Alessandro Bacchetta
L
A sideways look at the proton
pion
right
40/60
Measured asymmetries in DIS
HERMES Coll, hep-ex/0507013
Alessandro Bacchetta
A sideways look at the proton
41/60
Parton distribution functions
with transverse spin
Photon moves into the screen/
proton moves out of the screen
Sivers
-
Boer-Mulders
-
Transversity
-
Alessandro Bacchetta
A sideways look at the proton
42/60
Chromodynamic lensing
Burkardt, PRD 66 (02)
Long. view
Trans. view
left
quarks
proton
right
Alessandro Bacchetta
A sideways look at the proton
43/60
Chromodynamic lensing
Long. view
Trans. view
left
photon
right
NOTE: QCD tells us that the FSI has to be attractive, since
quark and remnants form a color antisymmetric state
Alessandro Bacchetta
A sideways look at the proton
44/60
Chromodynamic lensing
Long. view
Trans. view
left
photon
right
Alessandro Bacchetta
A sideways look at the proton
45/60
Distortions in transverse space
Long. view
Trans. view
left
quarks
proton
right
Alessandro Bacchetta
A sideways look at the proton
46/60
Distortions in transverse space
Long. view
Trans. view
left
quarks
proton
right
The presence of spin can distort the distribution of quarks in
transverse space (orbital angular momentum of quarks is required)
A distortion in the distribution of quarks in transverse space
can give rise to a nonzero Sivers function
Alessandro Bacchetta
A sideways look at the proton
47/60
Results from Lattice QCD
Sivers function expected to be:
•NEGATIVE for up quarks
•POSITIVE for down quarks
QCDSF/UKQCD Collab. (see e.g. hep-ph/05110032)
Alessandro Bacchetta
A sideways look at the proton
48/60
Data from Hermes and Compass
PROTON
HERMES, hep-ex/0507013
DEUTERON
HERMES, PRL 94 (05)
COMPASS, PRL 94 (05)
Alessandro Bacchetta
A sideways look at the proton
49/60
Different fits
Anselmino et al., hep-ph/0511017
[20] Anselmino et al., PRD72 (05)
[21] Vogelsang, Yuan, PRD72 (05)
[23] Collins et al., hep-ph/0510342
Alessandro Bacchetta
A sideways look at the proton
50/60
Factorization
and hadron-hadron collisions
Feynman diagrams & Factorization
lepton
lepton
proton
lepton
proton
pion
proton
antilepton
SIDIS
Drell-Yan
electron
pion
proton
pion
positron
pion
proton
pion
e–e+ to pions
Alessandro Bacchetta
A sideways look at the proton
p-p to pions
52/60
Sivers effect in SIDIS
Long. view
Trans. view
left
quarks
proton
right
Alessandro Bacchetta
A sideways look at the proton
53/60
Sivers effect in Drell-Yan
Long. view
Trans. view
left
photon
antiquark
proton
right
The Sivers effect gets an extra minus sign due to the difference
between initial and final state interactions. Impossible to predict
it in parton model.
Clear-cut prediction of QCD
Alessandro Bacchetta
A sideways look at the proton
Collins, PLB 536 (02)
54/60
Final/initial state interactions
q
q
q
q
Drell-Yan
SIDIS
q
pp to hadrons
q
A.B., Bomhof, Mulders, Pijlman, hep-ph/0505268
Alessandro Bacchetta
A sideways look at the proton
55/60
kT k-factorization
is broken ?
Is
T -factorization
My personal opinion: what is shown by Collins and Qiu is not
sufficient to make such a statement. Maybe new concepts (i.e.
“advanced” factorization and “generalized” universality) can
work.
Bomhof, Mulders, Pijlman, PLB596
A.B., Bomhof, Mulders, Pijlman, PRD72
Alessandro Bacchetta
A sideways look at the proton
56/60
An example
A.B., D’Alesio, Bomhof, Mulders, Murgia, hep-ph/0703153
p p jet X atRHIC
“Standard” factorization &
universality
“Generalized” factorization
& universality
Broken factorization?
Alessandro Bacchetta
A sideways look at the proton
57/60
Conclusions
• Transverse spin and transverse momentum
observables uncover a new dimension of the
structure of the nucleon
• Intense progress is taking place both from the
theoretical and experimental point of view
• Impact also on hadron colliders and unpolarized
physics
Alessandro Bacchetta
A sideways look at the proton
58/60